Xio-chun Xue,Yong-gng Yu,*,Jin-ming Xie

aSchool of Energy and Power Engineering,Nanjing University of Science and Technology,Nanjing,China

bLuzhou North Chemical Industry Corporation,Luzhou,China

The in fluence of nozzle diameters on the interaction characteristic of combustion-gas jets and liquid

Xiao-chun Xuea,Yong-gang Yua,*,Jin-ming Xieb

aSchool of Energy and Power Engineering,Nanjing University of Science and Technology,Nanjing,China

bLuzhou North Chemical Industry Corporation,Luzhou,China

A R T I C L E I N F O

Article history:

12 May 2017

Accepted 24 May 2017

Available online 28 May 2017

Fluid mechanics

Combustion-gases

Taylor cavities

Jet shape

Bulk-loaded propellant

To investigate the controlling method of interior ballistic stability of bulk-loaded propellant guns,the combustion-gas generator and cylindrical stepped-wall chamber are designed aiming at the injection processes of combustion-gases in liquid.The expansion courses of Taylor cavities and the turbulent mixing characteristic of gas-liquid are recorded by means of high speed photographic system.Based on the experiment,three-dimensional unsteady model on the interaction of gas and liquid is established to simulate expansion characteristics of twin combustion-gas jets in liquid under different nozzle diameters.The distribution regularities of characteristic parameter in jet field are obtained and analyzed. The results show the pressure,velocity and temperature distributions under different nozzle diameters are basically the same at the initial time.As time goes on,these characteristic parameters under different nozzle diameters have large differences.

?2017 Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).

1.Introduction

The researchers and scholars all over the world are concerning about gas jets in water in recent years.Its applications are so wide in the engineering technology,involving underwater welding and cutting,underwater missile launch and the bull-loaded propellant gun(BLPG)[1,2].Aiming at the fluid mechanics mechanism of underwater combustion-gas jets,predecessors had carried out a lot of researches.Dai[3]revealed the evolutionary processes of backattack of the gas jet by means of visualization experiments.Xu [4]tracked the gas-liquid interface byadopting the VOF model and did numerical simulation on flow field of combustion-gas jets in water without considering vaporization.Weiland[5]analyzed that the supersonic gas jet inwater is highly turbulent and unsteadyand obtained that when the shock wave inside the jet came across the unsteady gas-liquid interface,it reassembled the energy and then re flect back with impacting the nozzle surface.So the“back-attack”is actually a feedback phenomenon of shock wave.Guo[6]studied the gas-liquid complex flows of gas jets in water and indicated the gas jets are wobbling at random due to the effect of large scale energy exchange by gas-water mixing and entrainment,and the wobble effect is affected a lot by environment flow at the zone of established flow.In addition,based on the BLPG,the ignition method of combustion-gas jets with high temperature and high pressure at the breech is usually adopted and the liquid propellant filling in the combustion chamber is broken to form a certain burning surface under the effect of fluid instability.However,the ignition processes with this breakup mechanism of liquid propellant has a great random,just resulting in uncontrolled interior ballistic performance in the BLPG.To introduce some controlling means,Talley[7]proposed a method of using boundary shapes to restrain unsteady expansion on Taylor cavity in liquid propellant under the effect of combustion-gas jets ignition.Macpherson[8] analyzed the frequency spectrum of pressure fluctuation in the combustion chamber of the BLPG on the base of experimental studies and explored the reasons and mechanism of pressure fluctuation in different frequency bands in the expansion processes of combustion-gas jet.Adams[9]studied the gas-liquid mixing characteristic in tapered combustion chamber.Despirito[10,11] simulated accelerating extension processes of gas-cavity and liquid column formed under the effect of the combustion-gas jet in cylindrical stepped-wall combustion chamber by means of Navier-Stokes equation.Yu[12,13]analyzed the interaction characteristic of ignition combustion-gas jet and liquid medium in the twodimensional observation chamber from the aspect of cold state, and proved the restraint function of expanding step on unsteady expansion of gas jet.

Taking the multi-point ignition of BLPG for the engineering background,the cold state experiments of twin combustion-gas jets[14]are designed aiming at the interior ballistic process.On the basis of above studies,discussions mainly focus on characteristic parameters of jet field and turbulent mixing mechanism of combustion gas and liquid under the conditions of different nozzle diameters by using of the FLUENT software in this paper.In the bulk-loaded liquid propellant gun,the combustion is resulted by the fluid instability that is the velocity difference of gas-liquid to form the combustion surface.So,this paper focuses on the interaction of gas-liquid under cold-state condition and then we will add the combustion of liquid by the ignition of the gas jet in our future work.

2.Experimental device

The experimental device is composed of the combustion-gas generator and the cylindrical stepped-wall observation chamber, as shown in Fig.1 and Fig.2.Among that,the combustion-gas generator is composed of the combustion chamber with high pressure,fast-burning powder,copper seal film and twin nozzles.In the experimentalprocesses,the observation chamberand the combustion-gas generator are connected through a screw thread and the observation chamber is full of liquid.The fast-burning powder filling in the combustion chamber of high pressure is ignited by the pulse electric ignition system,and then generating combustion gases with high pressure and high temperature.When the pressure of combustion-gas increases to a certain threshold quickly,thecombustion-gasbreaksthroughthecopperseal filmand isinjected into liquid throughtwin nozzles.The experimentalseries processesarerecordedbymeansofhighspeedphotographicsystem. The experimental device is placed upward that the combustion-gas is injected from the bottom of the observation chamber and the top ofthechamberisconnectedwiththeatmosphere.Thestructuresize of the observation chamber is shown in Fig.2.The length(L)of the firstfourstepsis20mmandthetotallengthofobservationchamber is 110 mm The first cylindrical diameter is 40 mm,and the later cylindrical diametergrowsbyΔDbyeachstep.Theratioofdiameter increments of each step to the length of the step isΔD/L that is the structure factor of cylindrical stepped-wall observation chamber. The water is used as the liquid medium.

Fig.1.The combustion-gas generator.

Fig.2.The cylindrical stepped-wall observation chamber.

3.Mathematical models

In this calculation,twin combustion gases are assumed to be ideal gas and viscous gas jets,with a 3D expansion;the chemical reaction and phase change of high gases and liquid medium are not considered;the gravity of combustion gas is ignored;the turbulent mixing processes of gas-liquid are simulated usingk-ε model. Based on aboveassumptions,thecontrolling equationsare described as follows

(1)Equation of continuity

This model has two phases with gas and liquid respectively.The phase volume fraction is respectivelyα1andα2.Density is respectivelyρ1andρ2.Among that,Sαqis source item.Due to ignoring the chemicalreaction,Sαqis zero.And the volume fraction:

(2)Momentum conservation equation

Among that,

(3)Energy conservation equation

Among that

(4)Equation of state

(5)Turbulent flow equation

Among that,σkandσεare the turbulent Prandtl numbers forkand ε,respectively.-is Reynolds stress that expresses the in fluence of pulsation to time averaged flow.And the turbulent(oreddy)viscosity,μt,is computed bycombining andkand ε as follows

whereCμis a constant.

The model constants have the following default values

(6)Initial and boundary conditions

The computational domain of numerical simulation,whose size is designed by reference to experimental size,is showed in Fig.3. There are four types of boundaries,including pressure-inlet of combustion-gas,pressure-outlet,wall and symmetry.At the initial time,the combustion-gas jets have not been injected from twin nozzles,so the computational domain is initialized to the environmental parameters of liquid medium that isT=TO=300 K,p=po=101325Pa.The pressure value of the inlet is de fined by the experiment that isT=T1=2000K,p=p1=18 MPa.The outlet is connected with the atmosphere that isT=TO=300 K,p=po=101325Pa.The wall is under nonslip and adiabatic condition.The radial gradient at the symmetry is zero.

4.Numerical results and discussions

4.1.The comparison of numerical and experimental results

Fig.3.Computational domain.

One of numerical conditions adopts experimental condition that the injection pressure of combustion-gas is 18 MPa,the nozzle diameter is 1.5 mm,the nozzle distance is 16 mm and the structure factorΔD/L=0.6.The expansion processes of twin combustion-gas jets in liquid are simulated by Fluent.In the solver,the spatial attribute is 3D,the attribute of time is unsteady and the VOF modelis used to calculate multiphase flow.

Fig.5.Phase distribution under conditions ofd=0.8 mm,d=1 mm andd=1.5 mm (att=1 ms andt=4 ms).

Fig.4.The compassion of experimental and numerical results.

Fig.4(a)is the compassion of experimental photograph and numerical result when twin combustion-gas jets expand in the cylindrical stepped-wall chamber.It can be seen the numerical result is qualitatively in accordance with the experimental result. The axial expansion displacements are obtained by taking the average of the position of the front face of Taylor cavities under different times and the compassion curve is shown in Fig.4(b).As can see fromthe figure,they quantitativelyaccorded well with each other.In addition, finer grids are used to test the grid independence.We found that the displacements error can be controlled to within 1%when we continue increasing the grid numbers.The numerical results on axial displacement between different grid resolutions are little difference and only have an estimated maximum error of 1.8%.

4.2.Numerical discussions and analysis under different nozzle diameters

The injection pressure is 18 MPa,the nozzle distance is 16 mm, the structure factorΔD/L=0.6 and the nozzle diameters are 0.8 mm,1 mm and 1.5 mm respectively to simulate the turbulent mixing characteristic of twin combustion-gas jets and liquid under different nozzle diameters.Fig.5 is the density distribution of twin combustion-gas jets in liquid.

The interfaces between two phases can be seen from Fig.5.At the initial time,the density distribution characteristics under different nozzle diameters are basically the same.As twin combustion-gas jets expand and converge,when the nozzle diameter is larger,the entrainment phenomenon of boundaries of jets isn't more obvious and the Taylor cavities expand more fully along the radial direction of each step and the time when the jets reach to the outlet of observation chamber is shorter.When the nozzle diameter is 0.8 mm,aftertwin combustion-gas jets converge into one,the turbulent folds at the boundaries and heads of jets are very obvious and the fold layers evolve into entrainment phenomenon of droplet under the stretching and breaking of back flow effect.When the nozzle diameter is 1-1.5 mm,the heads of jets are smooth at 1-1.5 ms and the interfaces between two phases show turbulent folds just at the corner of each step.

Fig.6.Pressure distribution under conditions ofd=0.8 mm,d=1 mm andd=1.5 mm(att=1 ms andt=1.5 ms).

Fig.7.The pressure curve along axial direction.

Fig.6 shows the pressure distribution of twin combustion-gas jetsin liquid underdifferentnozzlediameters.When the combustion-gases are just injected into liquid medium that is 0～1 ms,the pressure structures under different diameters are basically the same and the pressure wave increases by degrees generally along the axial direction until two spherical waves with high pressure are former at the front face of Taylor cavities.While hemi-ellipsoidal pressure waves are formed along the radial direction and they decrease by degrees.Low pressure areas appear at the corner of each step under different nozzle diameter and these low pressure areas are just the areas where the corner vortices appear.The corner vortices and hemi-ellipsoidal pressure waves provide dynamic factors for radial expansion of jets.At 1.5 ms,the pressure distributions under different nozzle diameter have clear differences.When the nozzle diameter is 0.8 mm,the entrainment phenomenon of Taylor cavities is most obvious and thus the pressure pulsation is also most intense.When the nozzle diameter is 1 mm,twin high pressure areas at the front face of jets converge into one and pressure changes appear near the nozzle because of the necking effect of Taylor cavities.When the nozzle diameter is 1.5 mm,the pressure waves whose structures are still the same as that of previous pressure waves move downstream.As jets continue to expand,the pressure pulsation appears throughout whole jet field under the necking and expansion of jets and entrainment effects of droplets.When the jets expand to later period that is 4 ms,the larger the nozzle diameter is,the larger the pulsation areas of pressure along axial direction near twin nozzles and the more obvious the pulsation phenomenon is.

Combined with the pressure and phase distributions of jet field, the pressure curves are analyzed along axial and radial sections of observation chamber.Fig.7 is the pressure curve along central axis of the nozzle at 1 ms and 4 ms.At1 ms,the jets are just injected into liquid.The pressure values increase from negative minimum to the maximum by degrees and reach to maximum values of 0.256 MPa, 0.11 MPa and 0.103 MPa at axial displacements of 32 mm,36 mm and 37 mm respectively(corresponding to nozzle diameters of 0.8 mm,1 mm and 1.5 mm).It can be seen that from above data,the smaller the nozzle diameter is,the closer the high pressure areas are to twin nozzles and the larger is the pressure value which high pressure areas can reach to.At the downstream of jet field,the pressures all decrease to the environmental pressures by degrees. However,when the nozzle diameters are 1 mm-1.5 mm,the radial volumes of Taylor cavities are larger and boundaries of Taylor cavities are closer to the boundaries of the steppes,which result into a pressure pulsation at the downstream of high pressure areas under the in fluences of corner vortices.

At 4 ms,the outlet pressure decreases as the nozzle diameter increases.When the nozzle diameter is 0.8 mm,the outlet pressure reaches to 13.7 MPa,which is because the necking phenomenon has appeared since the jets are injected from twin nozzles.The pressure rises at the upstream of necking phenomenon.When the nozzle diameters are 1 mm and 1.5 mm,the pressures reach to the maximums of 6.595 MPa and 1.536 MPa at the axial displacement of 9 mm and 18 mm respectively.Combined with the density distribution,it can be seen the larger the nozzle diameter is,the smaller the necking degree is.Compared with 1 ms,a pressure pulsation appears near the nozzle as a result of necking effect.

Fig.8 is the radial velocity distributions of twin combustion-gas jets under different nozzle diameters.The plus direction is towards the observation wall and the minus direction is towards the central axis of the observation chamber.From the figure,the radial velocity distributions under different nozzle diameters are basically the same at the initial time.As time goes on,the radial velocities near each step are large.When the nozzle diameter is 0.8 mm,the discontinuityof radialvelocity distribution is largerat 1.5 ms.When the nozzle diameter is 1 mm-1.5 mm,the radial velocity distribution is also the same as that at previous time and the areas where the radial velocities reach to a larger value move towards the observation wall and downstream that the intervals of radial displacements are 11 mm-13 mm and 11.5 mm-14 mm respectively (corresponding to the nozzle diameters of 1 mm and 1.5 mm).

5.Conclusions

The conclusions are obtained according to above analysis and discussions

1)The density distribution characteristics under different nozzle diameters are basically the same at the initial time.As twin combustion-gas jets expand and converge,when the nozzle diameter is larger,the entrainment phenomenon of boundaries of jets isn't more obvious and the Taylor cavities expand more fully along the radial direction of each step and the time when the jets reach to the outlet of observation chamber is shorter. The corner vortices are all generated at each step underdifferent nozzle diameters.Just as a result of radial tractive effort of corner vortices,the fold layers appear at the interfaces of two phases of each step.In addition,the numerical data accord well with experimental data.

Fig.8.Radial distribution under conditions ofd=0.8 mm,d=1 mm andd=1.5 mm(att=1 ms andt=1.5 ms).

2)When twin combustion-gases are just injected into the liquid, the pressure wave structures under different nozzle diameters are basically the same.On the whole,the pressure wave increases by degrees generally along the axial direction until two spherical waves with high pressure are former at the front face of Taylor cavities.While hemi-ellipsoidal pressure waves are formed along the radial direction and they decrease by degrees.When the jets expand tolater period,the larger thenozzle diameter is,the larger the pulsation areas of pressure along axial direction near twin nozzles and the more obvious the pulsation phenomenon is.

3)When the nozzle diameter is 0.8 mm,the discontinuity of radial velocity distribution is larger at 1.5 ms.When the nozzle diameter is 1 mm-1.5 mm,the areas where the radial velocities reach to a larger value just move towards the observation wall and downstream at 1.5 ms.As the jets expand tothe laterperiod, the discontinuity of the radial velocity distribution is more obvious when the nozzle diameter is larger.

Acknowledgments

This work is supported by National Nature Science Foundation of China(No.51506096)and Foundation Research Project of Jiangsu Province(The Natural Science Fund No.BK20150765).

dimensionalgas-liquid two-phase flow using imageprocessmethod. J Hydrodyn 2006;18(2):127-34.

[2]Chang IS,Judd SJ.Air sparging of a submerged MBR for municipal wastewater treatment.Proc Biochem 2002;37:915-20.

[3]Dai ZQ,Wang BY,Qi LX,et al.Experimental study on hydrodynamic behaviors of high-speed gas jets in still water.Acta Mech Sin 2006;22(5):443-8.

[4]Xu XQ,Deng J,Ren AL.The research on high-speed gas jet of rocket nozzle underwater.J Hydrodyn 2005;17(2):204-8.

[5]Weiland C,Yagla J,Vlachos P.Submerged gas jet interface stability.In:Cd-ROM Proc.XXII ICTAM,vol.8;2008.p.25-9.Paper No.11872.

[6]Guo Q,Shi HH,Wang C.Study on gas-liquid complex flow induced by submerged supersonic gas jets.Chin J Eng Thermophys 2012;33(5):809-12.

[7]Talley RL,Owezarczak JA.Investigation of bulk-loaded liquid propellant gun concepts.ARL-CR-335.1998.

[8]A.K.Macpherson,A.J.Bracuti,Analysis of gun pressure instability,The 19th International Symposium on Ballistics.Switzerland,pp.115-121(2001).

[9]Adams M,Barth EJ.Dynamic modeling and design of a bulk-loaded liquid monopropellant powered ri fle.J Dyn Syst 2008;130(6):1-8.

[10]Despirito J.CFD analysis of the interior ballistics of the bulk-load liquid propellant.AIAA 96-3079.1996.

[11]DeSpirito J.Interior ballistic simulations of the bulk-loaded liquid propellant gun.ARL-TR-2316.2001.

[12]Yu YG,Yan SH.Study on expansion process and interaction of high speed twin combustion-gas jet in liquid.J Appl Mech 2010;77(5):051404-1-051404-7.

[13]Yu YG,Chang XX.Study of bulk-loaded liquid propellant combustion propulsion processes with stepped-wall combustion chamber.J Appl Mech 2011;78(5):051001-1-051001-8.

[14]Xue XC,Yu YG,Zhang Q.Study on expansion characteristic of twin combustion gas jets in five-stage cylindrical stepped-wall observation chamber.Flow Turbul Combust 2013;91(1):139-55.

[1]Zhao KY,Cheng W,Liao WL,et al.The void fraction distribution in two-

4 January 2017

*Corresponding author.

E-mail address:yygnjust801@163.com(Y.-g.Yu).

Peer review under responsibility of China Ordnance Society.

http://dx.doi.org/10.1016/j.dt.2017.05.016

2214-9147/?2017 Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

in revised form